Solve for $x$ and $y$ using elimination. ${2x+3y = 17}$ ${5x-4y = -15}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-5$ and the bottom equation by $2$ ${-10x-15y = -85}$ $10x-8y = -30$ Add the top and bottom equations together. $-23y = -115$ $\dfrac{-23y}{{-23}} = \dfrac{-115}{{-23}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {2x+3y = 17}\thinspace$ to find $x$ ${2x + 3}{(5)}{= 17}$ $2x+15 = 17$ $2x+15{-15} = 17{-15}$ $2x = 2$ $\dfrac{2x}{{2}} = \dfrac{2}{{2}}$ ${x = 1}$ You can also plug ${y = 5}$ into $\thinspace {5x-4y = -15}\thinspace$ and get the same answer for $x$ : ${5x - 4}{(5)}{= -15}$ ${x = 1}$